# An acidic solution of dichromate is electrolyzed

Question:

An acidic solution of dichromate is electrolyzed for 8 minutes using $2 \mathrm{~A}$ current. As per the following equation

$\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}+14 \mathrm{H}^{+}+6 \mathrm{e}^{-} \rightarrow 2 \mathrm{Cr}^{3+}+7 \mathrm{H}_{2} \mathrm{O}$

The amount of $\mathrm{Cr}^{3+}$ obtained was $0.104 \mathrm{~g}$. The efficiency of the process(in\%) is

(Take: $\mathrm{F}=96000 \mathrm{C}$, At. mass of chromium $=52$ )

Solution:

Moles of $\mathrm{e}^{\odot}=\left(\frac{8 \times 60 \times 2}{96000}\right)$

Using stoichiometry; theoritically

$\frac{\mathrm{n}_{\mathrm{e}} \text { used }}{6}=\frac{\mathrm{n}_{\mathrm{cr}^{+3}} \text { produced }}{2}$

$\Rightarrow \mathrm{n}_{\mathrm{cr}^{+3}}$ produced $=\frac{2}{6} \times \frac{8 \times 60 \times 2}{96000}$

$=\frac{0.02}{6}$

$\Rightarrow \mathrm{wt}_{\mathrm{cr}^{+3}}$ theoritically produced

$=\left(\frac{0.02}{6} \times 52\right) \mathrm{g}$

$\Rightarrow \%$ efficiency $=\frac{0.104 \mathrm{~g}}{\left(\frac{0.02 \times 52}{6}\right) \mathrm{g}} \times 100$

$=60 \%$